Engine fuel systems provide fuel to an engine from a fuel storage system. Generally, the amount of fuel provided to the engine is regulated using a fuel valve coupled to a fuel pump. Among other functions, fuel control systems are used to control the fuel pressure in an accumulator before the fuel is injected into an internal combustion engine. Fuel control systems are used to maintain a desired fuel pressure in an accumulator by actuating a fuel valve within an acceptable tolerance with respect to a desired fuel pressure for a given operating condition (e.g., engine power, engine speed, vehicle speed, etc.). However, problems may arise when a fuel control system is applied in a condition where the capacity of the pump is less than the amount of fuel being demanded by the engine.